3,340 research outputs found
The isomorphism problem for profinite completions of residually finite groups
We consider pairs of finitely presented, residually finite groups
. We prove that there is no algorithm that, given an
arbitrary such pair, can determine whether or not the associated map of
profinite completions is an
isomorphism. Nor do there exist algorithms that can decide whether is
surjective, or whether is isomorphic to .Comment: 12 page
On the difficulty of presenting finitely presentable groups
We exhibit classes of groups in which the word problem is uniformly solvable
but in which there is no algorithm that can compute finite presentations for
finitely presentable subgroups. Direct products of hyperbolic groups, groups of
integer matrices, and right-angled Coxeter groups form such classes. We discuss
related classes of groups in which there does exist an algorithm to compute
finite presentations for finitely presentable subgroups. We also construct a
finitely presented group that has a polynomial Dehn function but in which there
is no algorithm to compute the first Betti number of the finitely presentable
subgroups.Comment: Final version. To appear in GGD volume dedicated to Fritz Grunewal
Subgroup separability in residually free groups
We prove that the finitely presentable subgroups of residually free groups
are separable and that the subgroups of type are virtual
retracts. We describe a uniform solution to the membership problem for finitely
presentable subgroups of residually free groups.Comment: 8 pages, no figure
Limit groups, positive-genus towers and measure equivalence
By definition, an -residually free tower is positive-genus if all
surfaces used in its construction are of positive genus. We prove that every
limit group is virtually a subgroup of a positive-genus -residually
free tower. By combining this with results of Gaboriau, we prove that
elementarily free groups are measure equivalent to free groups.Comment: 10 pages; no figures. Minor changes; now to appear in Ergod. Th. &
Dynam. Sy
Pressure-dependent 13C chemical shifts in proteins: Origins and applications
Pressure-dependent (13)C chemical shifts have been measured for aliphatic carbons in barnase and Protein G. Up to 200 MPa (2 kbar), most shift changes are linear, demonstrating pressure-independent compressibilities. CH(3), CH(2) and CH carbon shifts change on average by +0.23, -0.09 and -0.18 ppm, respectively, due to a combination of bond shortening and changes in bond angles, the latter matching one explanation for the gamma-gauche effect. In addition, there is a residue-specific component, arising from both local compression and conformational change. To assess the relative magnitudes of these effects, residue-specific shift changes for protein G were converted into structural restraints and used to calculate the change in structure with pressure, using a genetic algorithm to convert shift changes into dihedral angle restraints. The results demonstrate that residual (13)C alpha shifts are dominated by dihedral angle changes and can be used to calculate structural change, whereas (13)C beta shifts retain significant dependence on local compression, making them less useful as structural restraints
Performance evaluation of the Boron Coated Straws detector with Geant4
The last decade has witnessed the development of several alternative neutron
detector technologies, as a consequence of upcoming neutron sources and
upgrades, as well the world-wide shortage of He. One branch of development
is the family of B-based gaseous detectors. This work focuses on the
boron coated straws (BCS) by Proportional Technologies Inc., a commercial
solution designed for use in homeland security and neutron science. A detailed
Geant4 simulation study of the BCS is presented, which investigates various
aspects of the detector performance, e.g. efficiency, activation, absorption
and the impact of scattering on the measured signal. The suitability of the BCS
detector for Small Angle Neutron Scattering (SANS), direct chopper spectrometry
and imaging is discussed.Comment: 50 pages, 37 figures, minor changes after review, results unchange
Suppression of intrinsic neutron background in the Multi-Grid detector
One of the key requirements for neutron scattering instruments is the
Signal-to-Background ratio (SBR). This is as well a design driving requirement
for many instruments at the European Spallation Source (ESS), which aspires to
be the brightest neutron source of the world. The SBR can be effectively
improved with background reduction. The Multi-Grid, a large-area thermal
neutron detector with a solid boron carbide converter, is a novel solution for
chopper spectrometers. This detector will be installed for the three
prospective chopper spectrometers at the ESS. As the Multi-Grid detector is a
large area detector with a complex structure, its intrinsic background and its
suppression via advanced shielding design should be investigated in its
complexity, as it cannot be naively calculated. The intrinsic scattered neutron
background and its effect on the SBR is determined via a detailed Monte Carlo
simulation for the Multi-Grid detector module, designed for the CSPEC
instrument at the ESS. The impact of the detector vessel and the neutron
entrance window on scattering is determined, revealing the importance of an
optimised internal detector shielding. The background-reducing capacity of
common shielding geometries, like side-shielding and end-shielding is
determined by using perfect absorber as shielding material, and common
shielding materials, like BC and Cd are also tested. On the basis of the
comparison of the effectiveness of the different shielding topologies and
materials, recommendations are given for a combined shielding of the Multi-Grid
detector module, optimised for increased SBR.Comment: 26 pages, 18 figures, revise
Higher Order Bases in a 2D Hybrid BEM/FEM Formulation
The advantages of using higher order, interpolatory basis functions are examined in the analysis of transverse electric (TE) plane wave scattering by homogeneous, dielectric cylinders. A boundary-element/finite-element (BEM/FEM) hybrid formulation is employed in which the interior dielectric region is modeled with the vector Helmholtz equation, and a radiation boundary condition is supplied by an Electric Field Integral Equation (EFIE). An efficient method of handling the singular self-term arising in the EFIE is presented. The iterative solution of the partially dense system of equations is obtained using the Quasi-Minimal Residual (QMR) algorithm with an Incomplete LU Threshold (ILUT) preconditioner. Numerical results are shown for the case of an incident wave impinging upon a square dielectric cylinder. The convergence of the solution is shown versus the number of unknowns as a function of the completeness order of the basis functions
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